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Bumek [7]
3 years ago
15

Inverse of m(x)=2x^2-6

Mathematics
1 answer:
romanna [79]3 years ago
6 0
m(x)=2x^2-6\to y=2x^2-6\ \ \ \ |add\ 6\ to\ both\ sides\\\\2x^2=y+6\ \ \ \ \ |divide\ both\ sides\ by\ 2\\\\x^2=\dfrac{y+6}{2}\ \ \ \ |sqare\ root\ both\ sides\\\\x=\sqrt{\dfrac{y+6}{2}}\\\\Answer:\boxed{m^{-1}(x)=\sqrt{\frac{x+6}{2}}\ for\ x\geq-6}
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The average monthly rainfall for 6 months was 28.5 mm. If it had rained 1mm more each month what would the average have been? By
Fynjy0 [20]

Answer:

29.5 mm

Step-by-step explanation:

We are told that the average monthly rainfall for 6 months was 28.5 mm.

Thus, total for the 6 months = 28.5 × 6 = 171 mm

Now, we are told that it rained 1 mm extra each month.

So extra for the six months = 1 × 6 = 6mm

New total for 6 months = 171 + 6 = 177 mm

So, new average for 6 months = 177/6 = 29.5 mm

4 0
3 years ago
A field bordering a straight stream is to be enclosed. The side bordering the stream is not to be fenced. If 1000 yards of fenci
sveta [45]

Answer:

x  =  500 yd

y  =  250 yd

A(max) = 125000 yd²

Step-by-step explanation:

Let´s call x the side parallel to the stream ( only one side to be fenced )

y the other side of the rectangular area

Then the perimeter of the  rectangle  is  p  =  2*x  + 2* y  ( but only 1 x will be fenced)

p  =  x  +  2*y

1000  =  x   +  2 * y         ⇒    y  =  (1000 - x )/ 2

And   A(r)  =  x * y

Are as fuction of x

A(x)  =  x  *  (  1000  -  x ) / 2

A(x)  =   1000*x / 2 -  x² / 2

A´(x)  =  500  -  2*x/2

A´(x)  =  0              500   -  x   =  0

x  =  500 yd

To find out if this value will bring function A to a maximum value we get the second derivative

C´´(x)  =  -1         C´´(x) < 0  then efectevly we got a maximum at  x  = 500

The side  y  = ( 1000  -  x ) / 2

y  =  500/ 2

y  =  250 yd

A(max)  =  250 * 500

A(max) = 125000 yd²

3 0
3 years ago
Last year, the school library had a total of x books. Over the summer, the library acquired another 35 books and now has a total
ki77a [65]

Answer:

the equation is x= 2908

Step-by-step explanation:

you need to find the number of books they had by taking the new total and subtract it by the number they add and that would equal x in the problem

6 0
3 years ago
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Answer:

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use the table to find each ratio 8 white socks and 6 black socks and 4 blue socks and 5 brown socks ... white socks to brown soc
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<h3>Answer:</h3>
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Each of the ratio components (white socks, brown socks, black socks, total socks) has an associated number (8, 5, 6, 23). Write the desired ratio using the associated numbers.

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